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A scientific scandal
Commentary; New York; Apr 2003; David Berlinski;

IN SCIENCE, as in life, it is always an excellent idea to cutthe cards after
the deck has been shuffled. One may admire the dealer, but trustis another
matter.In a recent essay in COMMENTARY, "Has Darwin Met HisMatch?" (December
2002), I discussed, evaluated, and criticized theories ofintelligent design,
which have presented the latest challenge to Darwin's theoryof evolution. In
the course of the discussion I observed that the evolution ofthe mammalian
eye has always seemed difficult to imagine. It is an issue thatDarwin himself
raised, and although he settled the matter to his ownsatisfaction, biologists
have long wished for a direct demonstration thatsomething like a functional
eye could be formed in reasonable periods of time bymeans of the Darwinian
principles of random variation and natural selection.Just such a
demonstration, I noted in my essay, is what thebiologists Dan-Erik Nilsson
and Susanne Pelger seemed to provide in a 1994paper.1 Given nothing more than
time and chance, a "lightsensitivepatch," they affirmed, can "gradually turn
into a focused-lenseye," and in the space of only a few hundred thousand
years-a mere moment,as such things go.Nilsson and Pelger's paper has, for
understand- able reasons,been widely circulated and widely praised, and in
the literature of evolutionarybiology it is now regularly cited as
definitive. Not the least of its remarkableauthority is derived from the
belief that it contains, in the words of one ofits defenders, a "computer
simulation of the eye's evolution."If this were true, it would provide an
extremely importantdefense of Darwin's theory. Although a computer simulation
is not by itselfconclusive-a simulation is one thing, reality another-it is
often an importantlink in an inferential chain. In the case of Darwin's
theory, the matter isespecially pressing since in the nature of things the
theory cannot be confirmedover geological time by any experimental procedure,
and it has proved verydifficult to confirm under laboratory conditions. The
claim that the eye'sevolution has been successfully simulated by means of
Darwinian principles, withresults falling well within time scales required by
the theory, is thus a matterof exceptional scientific importance.And not just
scientific importance, I might add; so dramatica confirmation of Darwinian
theory carries large implications for ourunderstanding of the human species
and its origins. This is no doubt why thestory of Nilsson and Pelger's
computer simulation has spread throughout theworld. Their study has been
cited in essays, textbooks, and popular treatmentsof Darwinism like River Out
of Eden by the famous Oxford evolutionist RichardDawkins; accounts of it have
made their way onto the Internet in severallanguages; it has been promoted to
the status of a certainty and reported asfact in the press, where it is
inevitably used to champion and vindicateDarwin's theory of evolution.In my
essay, I suggested that Nilsson and Pelger's argumentsare trivial and their
conclusions unsubstantiated. I also claimed thatrepresentations of their
paper by the scientific community have involved aserious, indeed a flagrant,
distortion of their work. But in a letter publishedin the March issue of
COMMENTARY, the physicist Matt Young, whom I singled outfor criticism (and
whose words I have quoted here), repeated and defended hischaracterization of
Nilsson and Pelger's work as a "computer simulation ofthe eye's evolution."
It is therefore necessary to set the matter straightin some detail.I hope
this exercise will help to reveal, with a certainuncomfortable clarity, just
how scientific orthodoxy works, and how it imposesits opinions on the
faithful.HERE IN their own words is the main argument of Nilsson andPelger's
paper:Theoretical considerations of eye design allow us to findroutes along
which the optical structure of the eye may have evolved. Ifselection
constantly favors an increase in the amount of detectable spatialinformation,
a light-sensitive patch will gradually turn into a focused-lens eyethrough
continuous small improvements in design. An upper limit for the numberof
generations required for the complete transformation can be calculated with
aminimum number of assumptions. Even with a consistently pessimistic
approach,the time required becomes amazingly short: only a few hundred
thousand years.And here is how they arrived at their conclusions. Thesetting
is "a single circular patch of light-sensitive cells"-aretina, in
effect-"which is bracketed and surrounded by dark pigment."A "protective
layer" lies above these light-sensitive cells, so thatthe pigment, the
light-sensitive cells, and the protective layer form a kind ofsandwich.
Concerning the lightsensitive patch itself, Nilsson and Pelger provideno
further details, indicating neither its size nor the number of cells it
mightcontain.What they do assume, if only implicitly, is that changes tothe
initial patch involve either a deformation of its shape or a thickening ofits
cells. The patch can be stretched, dimpled, and pulled or pushed around,
andcells may move closer to one another, like bond salesmen converging on
acustomer.So much for what changes. What is the change worth?
Assuming(reasonably enough) that an eye is an organ used in order to see,
Nilsson andPelger represent its value to an organism by a single quantitative
character orfunction, which they designate as "spatial resolution" or
"visualacuity"-- sharp sight, in short. Visual acuity confers an advantage on
anorganism, and so, in any generation, natural selection "constantly favorsan
increase in the amount of detectable spatial information."There are two ways
in which visual acuity may be increased inan initial light-sensitive patch:
a) by the "invagination" of thepatch, so that it becomes progressively more
concave and eventually forms theenclosed interior of a sphere; and b) by the
constriction of the sphere'saperture (the two rounded boundaries formed as
the flat patch undergoesinvagination). These changes may be represented on
sheets of high-school graphpaper on which two straight lines-the x and y axes
of the system-have beencrossed. On the first sheet, representing
invagination, visual acuity movesupward on one axis as invagination moves to
the right on the other; on thesecond sheet, visual acuity moves upward as
constriction moves to the right. Thecurves that result, Nilsson and Pelger
assert, are continuous and increasing.They do not hurdle over any gaps, and
they go steadily upward until they reach atheoretical maximum.The similar
shape of the two graphs notwithstanding,invagination and aperture
constriction exercise different effects on visualacuity. "Initially,
deepening of the pit"-i.e., invagination-"isby far the most efficient
strategy," Nilsson and Pelger write; "butwhen the pit depth equals the width,
aperture constriction becomes moreefficient than continued deepening of the
pit." From this, they concludethat natural selection would act "first to
favor depression andinvagination of the light-sensitive patch, and then
gradually change to favorconstriction of the aperture."THE RESULT is a
pin-hole eye, which is surely an improvementon no eye at all. But there
exists an aperture size beyond which visual acuitycannot be improved without
the introduction of a lens. Having done all that itcan do, the pin-hole eye
lapses. Cells within the light-sensitive sphere nowobligingly begin to
thicken themselves, bringing about a "localincrease" in the eye's refractive
index and so forming a lens. When thefocal length of the lens is 2.55 times
its radius-the so-called Mattiessenratio-the eye will have achieved, Nilsson
and Pelger write, the "idealsolution for a graded-index lens with a central
refractive index of 1.52."2Thereafter, the lens "changes its shape from
ellipsoidto spherical and moves to the center of curvature of the retina." A
flatiris "gradually forms by stretching of the original aperture," whilethe
"focal length of the lens ... gradually shortens, [until] it equals
thedistance to the retina ... producing a sharply focused image."
Theappearance of this spherical, graded-index lens, when placed in the center
ofcurvature of the retina, produces "virtually aberration-free imaging
overthe full 180 degrees of the visual field."The same assumptions that
governed invagination and apertureconstriction hold sway here as well.
Plotted against increasing lens formation,visual acuity moves smoothly and
steadily upward as a graded-index lens makesits appearance, changes its
shape, and moves to center stage. When thesetransformations have been
completed, the result is a "focused camera-typeeye with the geometry typical
for aquatic animals."One step remains. Nilsson and Pelger now
amalgamateinvagination, constriction, and lens formation into a
single"transformation," which they represent by juxtaposing, against
changesin visual acuity, changes to the original patch in increments of 1
percent. Theresulting curve, specifying quantitatively how much visual acuity
may bepurchased for each 1-percent unit of change, is ascending, increasing,
andstraight, rising like an arrow at an angle of roughly 45 degrees from its
pointof origin. Transformations are "optimal" in the sense that they
bringabout as much visual acuity as theoretically possible, with the
"geometryof each stage [setting] an upper limit to the spatial resolution of
theeye."It is the existence and shape of this fourth curve thatjustify their
claim that "a light-sensitive patch will gradually turn intoa focused-lens
eye through continuous small improvements in design"(emphasis added). This is
not the happiest formulation they could have chosen.HOW MUCH does the initial
light-sensitive patch have tochange in order to realize a focused camera-type
eye? And how long will it taketo do so? These are the questions now before
us.As I have mentioned, Nilsson and Pelger assume that theirinitial
light-sensitive patch changes in 1-percent steps. They illustrate
theprocedure with the example of a flat one-foot ruler that also changes
in1-percent steps. After the first step, the ruler will be one foot plus 1
percentof one foot long; after the second step, it will be 1-percent longer
than thelength just achieved; and so forth. It requires roughly 70 steps to
double aone-foot ruler in length. Putting the matter into symbols, 1.01^sup
70^~= 2.Nilsson and Pelger undertake a very similar calculation withrespect
to their initial light-sensitive patch. But since the patch is
athree-dimensional object, they are obliged to deal with three dimensions
ofchange. Growing in steps of 1 percent, their blob increases its length,
itscurvature, and its volume. When all of these changes are shoehorned
together,the patch will have increased in magnitude along some overall (but
unspecified)dimension.The chief claim of their paper now follows: to achieve
thevisual acuity that is characteristic of a "focused camera-type eye with
thegeometry typical for aquatic animals," it is necessary that an
initialpatch be made 80,129,540 times larger (or greater or grander) than it
originallywas. This number represents the magnitude of the blob's increase in
size. Howmany steps does that figure represent? Since 80,129,540 = 1.01^sup
1,829^,Nilsson and Pelger conclude that "altogether 1,829 steps of 1 percent
arerequired" to bring about the requisite transformation.These steps, it is
important to remember, do not representtemporal intervals. We still need to
assess how rapidly the advantagesrepresented by such a transformation would
spread in a population of organisms,and so answer the question of how long
the process takes. In order to do this,Nilsson and Pelger turn to population
genetics. The equation that followsinvolves the multiplication of four
numbers:R=h^sup 2^*i*V*mHere, R is the response (i.e. visual acuity in
eachgeneration), h is the coefficient of heredity, i designates the intensity
ofselection, V is the coefficient of variation (the ratio of the
standarddeviation to the mean), and m, the mean value for visual acuity.
These fournumbers designate the extent to which heredity is responsible for
visual acuity,the intensity with which selection acts to prize it, the way
its mean or averagevalue is spread over a population, and the mean or average
value itself. Valuesare assigned as estimates to the first three numbers; the
mean is leftundetermined, rising through each generation.As for the estimates
themselves, Nilsson and Pelger assumethat h^sup 2^=.50; that i = 0.01; and
that V= 0.01. On this basis, they concludethat R = 0.00005m. The response in
each new generation of light-sensitivepatches is 0.00005 times the mean value
of visual acuity in the previousgeneration of light-- sensitive patches.Their
overall estimate-the conclusion of their paper-nowfollows in two stages.
Assume that n represents the number of generationsrequired to transform a
light-sensitive patch into a "focused camera-typeeye with the geometry
typical for aquatic animals." (In small aquaticanimals,'a generation is
roughly a year.) If, as we have seen, the mean value ofvisual acuity of such
an eye is 1.01^sup 1,829^ = 80,129,540, where 1,829represents the number of
steps required and 80,129,540 describes the extent ofthe change those steps
bring about; and if 1.00005^sup n^ = 1.01^sup 1,829^ =80,129,540, then it
follows that n = 363,992.It is this figure-363,992-that allows Nilsson and
Pelger toconclude at last that "the time required [is] amazingly short: only
a fewhundred thousand years." And this also completes my exposition of
Nilssonand Pelger's paper. Business before pleasure.


John Landon
Website for
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